Evaluate the Determinant of a 2x2 Matrix with Step-by-Step Solution

Math Problem Statement

Evaluate the determinant of the 2x2 matrix.

The image shows a problem where a determinant of a 2x2 matrix needs to be evaluated. The matrix appears to be:

1 & 1 \\ -1 & 1 \end{bmatrix}$$ The determinant of a 2x2 matrix $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$ is calculated as: $$\text{Determinant} = (a \cdot d) - (b \cdot c)$$ Substituting the values: $$\text{Determinant} = (1 \cdot 1) - (1 \cdot -1)$$ $$\text{Determinant} = 1 - (-1) = 1 + 1 = 2$$ The determinant of the given matrix is **2**. Would you like further clarification or additional details? --- ### Related Questions: 1. How do you evaluate determinants for larger matrices? 2. What are the properties of determinants that make them useful in solving systems of equations? 3. Can the determinant of a matrix help determine if it's invertible? 4. What happens if a determinant is zero? How does that affect the matrix? 5. How do determinants relate to the area/volume of geometric shapes? ### Tip: When calculating determinants, always double-check the signs in subtraction, as errors often occur there!

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Linear Algebra
Determinants

Determinant of a 2x2 matrix: det(A) = (a * d) - (b * c)

Properties of Determinants

Grades 9-12

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